However, if you're predicting the next flip in a finite series of flips that has already occurred, it's actually more likely that you'll alternate between heads and tails.
...because heads occurring separately are on average balanced by heads occurring in long sequences; but limiting the length of the series puts a limit on the long sequences.
In other words, in infinite sequences, "heads preceeded by heads" and "heads preceeded by tails" would be in balance, but if you cut out a finite subsequence, if the first one was "head preceeded by head", by cutting out the subsequence you have reclassified it.
Am I correct, or is there more?
I don't think this is correct. See my reply to AstraSequi.
(But I'm not certain I've understood what you're proposing, and if I haven't then of course your analysis and mine could both be right.)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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